<?xml version="1.0"?>
<div class="add">

<b>let </b><font color="Maroon">S</font> be   <a href="analoaf.html#NM2">OAffinPlane</a>;<br/><b>let </b><font color="Maroon">x</font> be   <a href="struct_0.html#NM1">Element</a> of <font color="Maroon">S</font>;<br/><b>let </b><font color="Maroon">y</font> be   <a href="struct_0.html#NM1">Element</a> of <font color="Maroon">S</font>;<br/><b>let </b><font color="Maroon">z</font> be   <a href="struct_0.html#NM1">Element</a> of <font color="Maroon">S</font>;<br/><b>let </b><font color="Maroon">t</font> be   <a href="struct_0.html#NM1">Element</a> of <font color="Maroon">S</font>;<br/>









<b>assume </b><a NAME="E1:54"/>
not <font color="Maroon">x</font>,<font color="Maroon">y</font> <a href="diraf.html#R2" target="_self">'||'</a> <font color="Maroon">z</font>,<font color="Maroon">t</font>
 ;<br/>

<a NAME="E2:54"/><b>then </b>
( not <font color="Maroon">x</font>,<font color="Maroon">y</font> <a href="analoaf.html#R2">//</a> <font color="Maroon">z</font>,<font color="Maroon">t</font> &amp; not <font color="Maroon">x</font>,<font color="Maroon">y</font> <a href="analoaf.html#R2">//</a> <font color="Maroon">t</font>,<font color="Maroon">z</font> )
 
<b>by </b><i/>;<br/>
<b>then consider </b><font color="Maroon">u</font> being   <a href="struct_0.html#NM1">Element</a> of <font color="Maroon">S</font><b> such that </b><br/><a NAME="E4:54"/><i><font color="Green">E21</font></i>: 
( ( <font color="Maroon">x</font>,<font color="Maroon">y</font> <a href="analoaf.html#R2">//</a> <font color="Maroon">x</font>,<font color="Maroon">u</font> or <font color="Maroon">x</font>,<font color="Maroon">y</font> <a href="analoaf.html#R2">//</a> <font color="Maroon">u</font>,<font color="Maroon">x</font> ) &amp; ( <font color="Maroon">z</font>,<font color="Maroon">t</font> <a href="analoaf.html#R2">//</a> <font color="Maroon">z</font>,<font color="Maroon">u</font> or <font color="Maroon">z</font>,<font color="Maroon">t</font> <a href="analoaf.html#R2">//</a> <font color="Maroon">u</font>,<font color="Maroon">z</font> ) )
 <b>by </b><i><a class="ref" href="analoaf.html#D6">ANALOAF:def 6</a></i>;<br/>
<a NAME="E5:54"/>
( <font color="Maroon">x</font>,<font color="Maroon">y</font> <a href="diraf.html#R2" target="_self">'||'</a> <font color="Maroon">x</font>,<font color="Maroon">u</font> &amp; <font color="Maroon">z</font>,<font color="Maroon">t</font> <a href="diraf.html#R2" target="_self">'||'</a> <font color="Maroon">z</font>,<font color="Maroon">u</font> )
 
<b>by </b><i>, </i>;<br/>
<b>hence </b><a NAME="E6:54"/>
 ex <font color="Olive">u</font> being  <a href="struct_0.html#NM1">Element</a> of <font color="Maroon">S</font> st <br/>( <font color="Maroon">x</font>,<font color="Maroon">y</font> <a href="diraf.html#R2" target="_self">'||'</a> <font color="Maroon">x</font>,<font color="Olive">u</font> &amp; <font color="Maroon">z</font>,<font color="Maroon">t</font> <a href="diraf.html#R2" target="_self">'||'</a> <font color="Maroon">z</font>,<font color="Olive">u</font> )
 ;<br/>


</div>
